Demodulation process for binary data

ABSTRACT

Two signals at different frequencies are optionally amplified or attenuated in an automatic gain control amplifier (1) after their reception, then separated from each other by means of band pass filters (2, 5) and amplitude-modulated by means of envelope curve detectors (3, 6), whereupon the envelope curve signals (z 0  [t], z 1  [t]) are sampled by means of sampling switches (4, 7) once per bit to produce sample values (z 0  [kT b  ], z 1  [kT b  ]) which are passed to a calculator unit (8) whose memory stores values of a decision table which are derived from a probability table. Each table area of the latter contains two probability values of which a first is the probability that the sample values (z 0  [kT b  ], z 1  [kT b  ]) lie in the respective table area if the first signal were sent and a second is the probability that the sample values (z 0  [kT b  ], z 1  [kT b  ]) lie in the respective table area if the second signal were sent. Set down in a table area of the decision table is a respective first logic value if the first probability value is greater than the second probability value and a respective second logic value if the first probability value is less than or equal to the second probability value. The process combines the advantages of the noncoherent demodulation process and the spread spectrum process.

FIELD OF THE INVENTION

The invention relates to a demodulation process for binary data, inparticular binary data which are transmitted by means of a frequencyshift keying process by way of a transmission channel, wherein twoshifted transmitted sinusoidal signals of different frequencies, afterreception, are first separated from each other in terms of frequency andthen separately amplitude-modulated for the purposes of producing twoenvelope curve signals.

BACKGROUND OF THE INVENTION

The demodulation process according to the invention may be used inreceivers, preferably in relation to transmissions in which the noisepower density spectrum of a transmission channel used, as a function ofthe frequency f, is not constant, and its characteristic is also notknown to the receivers. Under those circumstances it is not possible toselect two frequencies of a frequency shift keying process, so that thenoise power density spectra of the transmission channel are as small aspossible at the two frequencies, that is to say, two shifted signals ofthe frequency shift keying process, which belong to the two frequenciesand which are both a respective function of the time are disturbed aslittle as possible. On the contrary it is to be expected that--if thetwo frequencies are close together, as is usual in a conventionalfrequency shift keying process--both shifted signals occur in a severelydisturbed frequency range. For such situations, the use if possible of aspread band process (or "spread spectrum" process) is recommended in theliterature, for example in the book "Digital Communications and SpreadSpectrum Systems", R. E. Ziemer and R. L. Peterson, Macmillan PublishingCompany, New York, 1985, pages 327 to 328. However such processes sufferfrom the disadvantage that they are expensive to carry into effect.

A process of the kind to which this invention relates is known from thepublication IEEE Trans. on Communications, Sept. 86, Vol. COM-34, No. 9"Minimax Noncoherent Detection of BFSK Signals in Nonwhite GaussianNoise", T. Schaub and B. Steinle, pages 955 to 958, in which it is shownthat if the ratio of the noise power densities at the two frequencies isnot unity (see FIG. 1), a conventional noncoherent frequency shiftkeying receiver supplies the same reception results as if the twoshifted signals were disturbed, with the same mean noise power density.Also shown therein is a possible solution as to the way in which, forthe case of non unity noise power density ratio, the bit errorprobability of the transmitted binary data can be reduced, in comparisonwith the case where the ratio is unity. For that purpose, two weightingfactors, with which the two shifted signals are multiplied, after theyhave first been previously separated from each other in the receiver andamplitude-modulated, are optimised.

The invention is based on the problem of improving the knowndemodulation process and realising a demodulation process which combinesthe simplicity of the noncoherent demodulation process with theadvantages of the spread spectrum process.

SUMMARY OF THE INVENTION

(i) the values of the frequencies of the two shifted signals areselected to be so far apart that the latter are disturbed independentlyof each other and that as far as possible at least one of the twofrequencies lies in a weakly disturbed frequency range of thetransmission channel;

(ii) the two envelope curve signals are sampled once per bit for thepurposes of producing their sample values;

(iii) the sample values are passed to a calculator unit in whose memoryvalues of a decision table are stored, which values are derived from thevalues of a probability table;

(iv) for the purposes of drawing up the probability table the valuerange of the sample values of each respective envelope curve signal iseach in itself divided by means of threshold values into a plurality ofquantisation intervals which are plotted along respective ones of twocoordinate axes of the probability table for the purposes of forming thetable areas thereof;

(v) for each table area of the probability table a first probabilityvalue and a second probability value are calculated and specified in therespective table area, wherein the first probability value is theprobability that the sample values lie in the respective table area ifthe first shifted signal were sent and the second probability value isthe probability that the sample values lie in the respective table areaif the second shifted signal were sent;

(vi) a first logic value representing the first signal is set down in atable area of the decision table which has the same threshold values andas many table areas as the probability table if the first probabilityvalue is greater than the second probability value, and a second logicvalue representing the second shifted signal is set down if the firstprobability value is less than or equal to the second probability valueand;

(vii) the calculator unit ascertains in which table area of the decisiontable the supplied sample values lie, whereupon it is then deduced fromthe logic value contained in the respective table area of the decisiontable whether the first or the second shifted signal was most probablysent and is therefore to be considered as the received signal.

Preferred features of the present invention are set forth in theappended claims.

BRIEF DESCRIPTION OF THE INVENTION

FIG. 1 is a frequency spectrum diagram of useful and interferencesignals,

FIG. 2 shows a block circuit diagram of an arrangement for carrying outthe demodulation process according to the invention,

FIG. 3 shows a frequency spectrum diagram of interference and attenuateduseful signals prior to fading compensation, and

FIG. 4 shows a frequency spectrum diagram of interference and attenuateduseful signals after fading compression.

The same reference numerals identify the same parts in all the Figuresof the drawing.

It is assumed hereinafter that binary data are transmitted by means of afrequency shift keying process by way of a transmission channel whosetransmission properties alter with frequency f.

Transmission is effected by means of what is known as a BFSK-process("Binary Frequency Shift Keying" process), that is to say a frequencyshift keying process in which a shift is made between a first sinusoidalsignal s₀ [t] at the frequency f₀ and a second sinusoidal signal s₁ [t]at the frequency f₁ at the rhythm of the binary data to be transmitted,that is to say at the rhythm of the bits to be transmitted, the twofrequencies f₀ and f₁ being different. In that respect the firstsinusoidal signal s₀ [t] corresponds for example to a logic value "0"while the second sinusoidal signal s₁ [t] corresponds to a logic value"1".

The two signals s₀ [t] and s₁ [t] are only present during one or morebit durations in the form of carrier-frequency pulses and the band widthof their respective frequency spectrum S₀ [f] and S₁ [f] is restricted.The frequency spectra S₀ [f] and S₁ [f] are in that case eachsymmetrical with respect to the frequencies f₀ and f₁ of the firstsignal s₀ [t] and the second signal s₁ [t] respectively. A noise powerdensity spectrum G[f] and a respective frequency spectrum S₀ [f] and S₁[f] of the two signals s₀ [t] and s₁ [t] are shown in FIG. 1 as afunction of the frequency f. The latter each have a main band andsecondary bands, wherein the main band respectively has the frequency f₀and f₁ as the centre frequency and all secondary bands extendsymmetrically relative to the associated frequency f₀ and f₁respectively. The noise power density spectrum G[f] represents additivenonwhite Gaussian noise.

It has been assumed in FIG. 1, for the sake of simplicity of thedrawing, that the entire frequency range comprises only a firstfrequency range and a second frequency range, in each of which there isa respective constant power noise density spectrum G[f]=n₀ and G[f]=n₁,with n₁ being significantly smaller than n₀. In the demodulation processaccording to the invention the values of the two frequencies f₀ and f₁are selected to be far apart. FIG. 1 showed as a possible case the casein which the entire frequency spectrum S₀ [f] of the first signal s₀ [t]is contained entirely in the first frequency range and that S₁ [f] ofthe second signal s₁ [t] is contained entirely in the second frequencyrange. In that situation the two signals s₀ [t] and s₁ [t] areindividually disturbed by the additive white Gaussian noise which, atthe two frequencies f₀ and f₁, has a different noise power density n₀and n₁ respectively. The two signals s₀ [t] and s₁ [t] are thusdisturbed to different degrees upon transmission. The ratio n₁ /n₀ isreferred to hereinafter by x. It was also assumed in FIG. 1 that the twosignals s₀ [t] and s₁ [t] are attenuated to equal degrees in thetransmission channel so that the amplitudes of S₀ [f] and S₁ [f] are ofapproximately equal values.

The following apply:

    s.sub.0 [t]=[E.sub.b /2T.sub.b ].sup.1/2 ·cos[2πf.sub.0 t] and

    s.sub.1 [t]=[E.sub.b /2T.sub.b ].sup.1/2 ·cos[2πf.sub.1 t],

wherein E_(b) denotes the energy per transmitted bit and T_(b) denotesthe bit duration.

For the reception process, a noncoherent demodulation process is used inthe receivers as the receivers generally do not know the phase positionof the signals s₀ [t] and s₁ [t] sent. In principle however it is alsopossible to use the demodulation process according to the invention inrelation to a coherent demodulation procedure.

The following assumptions apply in regard to an example of calculationas set out hereinafter:

the frequency range available for the transmission comprises twofrequency ranges of equal size, in each of which there is a respectiveinterference signal with a noise power density n₀ and n₁ respectively,

x=n₁ /n₀ =-10 dB so that the first frequency range is heavily disturbedand the second frequency range is weakly disturbed,

E_(b) /n=2E_(b) /[n₀ +n₁ ]=6 dB, which corresponds to

E_(b) /n₀ =3.4 dB and

E_(b) /n₁ =13.4 dB;

the probability in regard to the occurrence of a heavily disturbed rangeis 50% and the probability for the occurrence of a weakly disturbedrange is also 50%.

In a conventional frequency shift keying process in which thefrequencies f₀ and f₁ are as close together as possible, there is both a50% probability that the frequencies f₀ and f₁ are both in the firstfrequency range and also a 50% probability that they are in the secondfrequency range. Corresponding thereto, when using a noncoherentdemodulation process, is a bit error probability of

    P.sub.e0 =0.5.exp[-0.5.E.sub.b /n.sub.0 ]=0 . 167

in the first frequency range and

    P.sub.e1 =0.5.exp[-0.5.E.sub.b /n.sub.1 ]=8.8 . 10.sup.-6

in the second frequency range so that with a 50% probability there is nomeaningful transmission (see the value of P_(e0)) while with a 50%probability there is a very good transmission (see the value of P_(e1)).

In the process according to the invention on the other hand thefrequencies f₀ and f₁ are as far as possible random and are selected tobe so far apart that there are the following three possibilities:

there is a 25% probability that the frequencies f₀ and f₁ both lie in aweakly disturbed frequency range. An error probability of P_(e1) =8.8 .10⁻⁶ corresponds thereto;

there is a 50% probability that the frequencies f₀ and f₁ each lie in adifferent frequency range. Corresponding thereto is an error probabilityof P_(e2) =1.22 . 10⁻³. The precise calculation of P_(e2) is describedhereinafter as an example of calculation in respect of equation IX;

there is a 25% probability that the frequencies f₀ and f₁ both lie in aseverely disturbed frequency range. An error probability of P_(e0) =0 .167 corresponds thereto.

That means that the probability that at least one of the two frequenciesf₀ and f₁ and therewith also at least one of the two frequency spectraS₀ [f] and S₁ [f] of the two signals s₀ [t] and s₁ [t] lies in theweakly disturbed frequency range rises from 50% to 75% so that in thiscase there is a good transmission while the probability of no meaningfultransmission is reduced to 25%. The values of the frequencies f₀ and f₁of the two signals s₀ [t] and s₁ [t] are thus selected to be so farapart that the latter are disturbed independently of each other and asfar as possible at least one of the two frequencies f₀ and f₁ lies in aweakly disturbed frequency range of the transmission channel.

The arrangement shown in FIG. 2 for carrying out the demodulationprocess according to the invention comprises an optical common fadingcompensation amplifier 1 ("Automatic Gain Control Amplifier"), a firstband pass filter 2 for the first signal s₀ [t] with an associated firstenvelope curve detector 3 which is disposed on the output side thereofand which has on its output side an associated first sampling switch 4,a second band pass filter 5 for the second signal s₁ [t] with anassociated second envelope curve detector 6 disposed on the output sidethereof and having on its output side an associated second samplingswitch 7, and a calculator unit 8. The input of the arrangement or, ifprovided, the output of the common automatic gain control amplifier 1are connected to the inputs of the two band pass filters 2 and 5, theoutputs of which are taken by way of the respectively associatedenvelope curve detectors 3 and 6 to the associated sampling switches 4and 7 respectively, the outputs of which are in turn each connected to arespective separate input of the common calculator unit 8. An output ofthe latter is also connected to the two control inputs of the samplingswitches 4 and 7. The centre frequency of the first band pass filter 2is equal to the frequency f₀ of the first signal s₀ [t] and that of thesecond band pass filter 5 is equal to the frequency f₁ of the secondsignal s₁ [t]. The band pass filter 2 and the envelope curve detector 3as well as the band pass filter 5 and the envelope curve detector 6 mayalso each be replaced by a per se known quadrature detector. Thestructure of the automatic gain control amplifier 1 is known per se andis shown for example in the book "Elements of ElectronicCommunications", 1978, J. J. Carr, Reston Publishing Company, Inc.,Reston, Va., USA, FIG. 21.7.

The two transmitted and shifted sinusoidal signals s₀ [t] and s₁ [t],after they are received in the receiver, are first separated from eachother in terms of frequency by means of the band pass filters 2 and 5and then separately amplitude-modulated in the respectively associatedenvelope curve detectors 3 and 6 in order to produce at the output ofthe latter a first envelope curve signal z₀ [t] and a second envelopecurve signal z₁ [t] respectively. Each envelope curve signal z₀ [t] andz₁ [t] is sampled by means of the associated sampling switch 4 and 7once per bit at the bit centre in order to obtain sample values z₀[kT_(b) ] of the first envelope curve signal z₀ [t] and sample values z₁[kT_(b) ] of the second envelope curve signals z₁ [t], wherein krepresents a serial number of the transmitted bits contained in thesignals s₀ [t], s₁ [t] and z₀ [t] and z₁ [t]. The sample values z₀[kT_(b) ] and z₁ [kT_(b) ] are passed to the calculator unit 8.

For the purposes of drawing up a probability table, the value range inwhich the sample values z₀ [kT_(b) ] and z₁ [kT_(b) ] of the twoenvelope curve signals z₀ [t] and z₁ [t] can lie, is each divided initself by means of threshold values w₀,i and w₁,j, into a plurality of,for example N₀ and N₁, quatisation intervals which are each plottedalong a respective one of two coordinate axes of the probability table,for the purposes of forming the table areas i;j thereof. In that respecti=0, 1,1 2, . . . , N₀ and j=0, 1, 2, . . . , N_(i), with w₀,0 =w₁,0 =0and w₀,N0 =w₁,N1 =infinite.

The number of quantisation intervals N₀ and N₁ are preferably the same.It is assumed hereinafter that N₀ =N₁ =4. In that case w₀,i =1.2.i.√[n₀.B_(T) ] and w₁,j =1.2.j.√[n₁.B_(T) ] for the values i and j of 1to N₀ -1 and 1 to N₁ -1, wherein B_(T) =1/T_(b) identifies the bandwidth of the filters 2 and 5 contained in the receiver.

The calculator unit 8 includes a computer, preferably a microcomputer,in the memory of which the values of a decision table are fixedlystored. In that respect the values of the decision table are derivedfrom the values of the probability table which for example looks likethe following when E_(b) /n=6 dB and x=-10 dB. ##STR1##

In that connection each table area i;j of the probability table has thefollowing content: ##STR2##

In the probability table the quantisation intervals of the sample valuesz₀ [kT_(b) ] and z₁ [kT_(b) ] of the two envelope curve signals z₀ [t]and z₁ [t] are plotted along two coordinate axes which extendperpendicularly to each other, for example the quantisation intervals ofthe sample values z₀ [kT_(b) ] are plotted along the abscissa and thoseof the sample values z₁ [kT_(b) ] are plotted along the ordinate.Disposed on the abscissa of the probability table are the thresholdvalues w₀,0 =0, w₀,1, w₀,2 and w₀,3 of the sample values z₀ [kT_(b) ]while disposed on the ordinate are the threshold values w₁,0 =0, w₁,1,w₁,2 and w₁,3 of the sample values z₁ [kT_(b) ].

The probability takes has N₀.N₁ =16 table areas i;j. For each of thetable areas i;j, a first probability value P₀ [i,j] and a secondprobability value P₁ [i,j] are calculated and specified in theappropriate table area i;j. The first probability value P₀ [i,j] is tobe found for example in a first line and the second probability value P₁[i,j] is to be found for example in a second line therebeneath. In thatconnection i is the second index of that threshold value w₀,i of thesample values z₀ [kT_(b) ] and j is the second index of that thresholdvalue w_(i),j of the sample values z₁ [kT_(b) ], which both define thetable area i;j towards the lower values while the upper limit valueshave i+1 and j+1 as an index. For example the table area 2;3 is defineddownwardly by the threshold values w₀,2 and w₁,3. The first probabilityvalue P₀ [i,j] is the probability that the two sample values z₀ [kT_(b)] and z₁ [kT_(b) ] of the envelope curve signals z₀ [t] and z₁ [t] liein the corresponding table area i;j if the first signal s₀ [t] were sentwhile the second probability value P₁ [i,j] is the probability that thetwo sample values z₀ [kT_(b) ] and z₁ [kT_(b) ] of the envelope curvesignals z₀ [t] and z₁ [t] lie in the respective area i;j if the secondsignal s₁ [t] were sent.

In other words:

P_(o) [i,j] is the probability that both w₀,i ≦z₀ ]kT_(b) ]<w₀,i+1 andalso w₁,j ≦z₁ [kT_(b) ]<w₁,i+1, if the first signal s₀ [t] were sent;

P₁ [i,j] in contrast is the probability that both w₀,i ≦z₀ [kT_(b)]<w₀,i+1 was also w₁,j ≦z₁ [kT_(b) ]<w₁,j+1, if the second signal s₁ [t]were sent;

P₀ [i,j] and P₁ [i,j] are thus the calculated probabilities that thepair of sample values z₀ [kT_(b) ] and z₁ [kT_(b) ] lies in the tablearea [i;j] on the assumption that the first signal s₀ [t] and that thesecond signal s₁ [t] were sent respectively.

The decision table which is derived from the probability table containsoptimum decisions for the various table areas i;j and is for example ofthe following appearance, again on the assumption that E_(b) /n=6 dB andx=-10 dB. ##STR3##

The decision table has the same threshold values w₀,1 and w₁,j and asmany N₀.N₁ table area i;j as the probability table and is drawn up usingthe "principle of maximum probability" (also referred to as the "MaximumLikelihood Principle") for the emitted signal s₀ [t] and s₁ [t] uponreception of the sample pair z₀ [kT_(b) ]; z₁ [kT_(b) ]. A first logicvalue, for example "0", which represents the first signal s₀ [t] is laiddown in a table area i;j of the decision table if the first probabilityvalue P₀ [i,j] is greater than the second probability value P₁ [i,j],while a second logic value, for example "1", which represents the secondsignal s₁ [t] is laid down if the first probability value P₀ [i,j] islower than or equal to the second probability value P₁ [i,j]. The logicvalue "0 " in that respect means that it is most probable that it wasthe first signal s₀ [t] that was sent and the logic value "1" means thatit was most probable that it was the second signal s₁ [t] that was sent.

The sample values z₀ [kT_(b) ] and z₁ [kT_(b) ] of the two envelopecurve signals z₀ [t] and z₁ [t] are passed in the calculator unit 8 tothe computer which ascertains in which table area i;j of the decisiontable the supplied sample values z₀ [kT_(b) ] and z₁ [kT_(b) ] lie,whereupon it then deduces from the logic value "0" or "1" contained inthe respective table area i;j whether it was most probable that it wasthe first or the second signal s₀ [t] or s₁ [t] that was sent and istherefore to be deemed to be the received signal. If for example z₀[kT_(b) ] is between the value w₀,0 =0 and the value w₀.1 and z₁ [kT_(b)] is between the value w₁,1 and the value w₁,2, then the optimumdecision is in accordance with the decision table represented; firstsignal s₀ [t] was most probably sent as a logic value "0" applies inrespect of the appropriate table area i;j. If on the other hand forexample z₁ [kT_(b) ] is above the value w₁,3, then the optimum decisionof the decision table represented is: the second signal s₁ [t] was mostprobably sent as a logic value "1" applies in respect of thecorresponding table area i;j.

The novelty of the arrangement according to the invention lies in thefact that the sample values z₀ [kT_(b) ] and z₁ [kT_(b) ] of theenvelope curve signals z₀ [t] and s₁ [t] of the two envelope curvedetectors 3 and 6 are not compared to each other by means of an analogcomparator as in a conventional demodulation process, so that thereceiver can decide for that signal s₀ [t] and s₁ [t] respectively asthe signal which it was most probable was sent, whose received envelopecurve has the greater amplitude, but that the calculator unit 8clarifies in which table area i;j of the decision table the samplevalues z₀ [kT_(b) ] and z₁ [kT_(b) ] are to be found and, on that basis,the signal s₀ [t] and s₁ [t] which is more probable for that table areai;j is deemed to be that signal which was sent.

In order to simplify the notation used and to shorten the followingequations, hereinafter z₀ [kT_(b) ] is replaced by z₀, z₁ [kT_(b) ] isreplaced by z₁, s₀ [t] is replaced by s₀ and s₁ [t] is replaced by s₁.

That then gives the following: ##EQU1## As z₀ and z₁ are statisticallyindependent of each other, the following also apply: ##EQU2##

In that connection the functions f_(z0/s0) [z₀ ], f_(z1/s0) [z₁ ],f_(z0/s1) [z₀ ] and f_(z1/s1) [z₁ ] represent the probability densityfunction for z₀ and z₁ respectively, on the assumption that s₀ and s₁respectively were sent.

On the assumption that the disturbance sources acting on thetransmission channel involve Gaussian distribution and are additivelyeffective, the following equations apply:

    f.sub.z0/s0 [z.sub.0 ]=[z.sub.0 /(n.sub.0.B.sub.T)].I.sub.0 [(A.z.sub.0)/(n.sub.0.B.sub.T)]. exp[-(z.sub.0.sup.2 +A.sup.2)/(2n.sub.0.B.sub.T)]                             (V),

    f.sub.z0/s1 [z.sub.0 ]=[z.sub.0 /(n.sub.0.B.sub.T)]. exp[-z.sub.0.sup.2 /(2n.sub.0.B.sub.T)]                                      (VI),

    f.sub.z1/s1 [z.sub.1 ]=z.sub.1 /(n.sub.1.B.sub.T)].I.sub.0 [(A.z.sub.1)/(n.sub.1.B.sub.T)]. exp[-(z.sub.1.sup.2 +A.sup.2)/(2n.sub.1.B.sub.T)]                             (VII)

    and

    f.sub.z1/s0 [z.sub.0 ]=[z.sub.1 /(n.sub.1.B.sub.T)]. exp[-z.sub.1.sup.2 /(2n.sub.1.B.sub.T)]                                      (VIII),

with z₀ >0 and z₁ >0 respectively. In that connection A is the amplitudeof the undisturbed signal and I₀ [x] is the modified Bessel function ofzero order.

The probability that false detection of the bit value occurs in thereceiver corresponds to the probability that the sample values z₀ and z₁lie in a table area i;j in which in the decision table there is a logicvalue "1", although the first signal s₀ was sent, and that they lie in atable area i;j in which in the decision table there is a logic value "0"although the second s₁ was sent. ##EQU3## Therein {P₀ [i,j], P₁[i,j]}_(min) identifies the smallest of the two probability values P₀[i,j] and P₁ [i,j] contained in a table area i;j of the probabilitytable. The probability value P_(e) corresponds to half the total valueof all those smallest probability values contained in all table areas ofthe probability table.

For N₀ =N₁ =4, the above-indicated probability table gives the followingvalue for P_(e) : ##EQU4##

For extreme cases, as for example x being approximately equal to one orx being very much greater than or very much smaller than one, thedemodulation process according to the invention is reduced to aconventional frequency shift keying (FSK) or a conventional amplitudeshift keying (ASK) demodulation process.

Then, for the case "x approximately equal to one", the decisioncriterion applies in the receiver: the first signal s₀ [t] was sent ifz₀ [kT_(b) ]≧z₁ [kT_(b) ], or the second signal s₁ [t] was sent if z₀[kT_(b) ]<z₁ [kT_(b) ].

For the case "x much smaller than one" and thus "n₁ much smaller than n₀", the following decision criterion applies in the receiver: the secondsignal s₁ [t] was sent if z₁ [kT_(b) ]≧T₀, and the first signal s₀ [t]was sent if z₁ [kT_(b) ]<T₀. In that case therefore only the samplevalues z₁ [kT_(B) ] of the weekly disturbed signal are used for thedecision.

For the case "x much smaller than one" and thus "n₁ much greater than n₀" the following decision criterion applies in the receiver: the firstsignal s₀ [t] was sent if z₀ [kT_(b) ]≧T₁ and the second signal s₁ [t]was sent if z₀ [kT_(b) ]<T₁. In that case therefore only the samplevalues z₀ [kT_(b) ] of the weekly disturbed signal are used for thedecision.

In that connection T₀ and T₁ are predetermined threshold values whichare preferably of the following value: T₀ =T₁ =√[(E_(b).B_(T))/2].

If an error-detecting or an error-correcting code is used in thetransmission, then disposed downstream of the calculator unit 8 is anerror-detecting or error-correcting arrangement which possibly permitswhat are known as "soft decisions". In the case of the latter,consideration is given not only to the logic values "1" and "0" whichare ascertained by the demodulation process, but also the probabilitieswith which those ascertained logic values "1" and "1" coincide with thetransmitted logic values. In that case the memory of the calculator unit8, alone or as a supplement to the content of the decision table, storesthe content of a metric table, for example preferably the content of theprobability table; the latter may contain the probabilities in quantisedor in logarithmed form. In the latter case the logarithmic values of theprobabilities are present in the probability table. In those casestherefore the probability value (P₀ [i,j], P₁ [i,j]) which are containedin the probability table or the logarithms of the probability values (P₀[i,j] , P₁ [i,j]) contained in the probability table are stored in thememory of the calculator unit 8, in order for them to be taken intoaccount in ascertaining the signal s₀ [t] or s₁ [t] which was mostprobably sent.

The application of the demodulation process according to the inventionis not just restricted to transmission channels in which the two signalss₀ [t] and s₁ [t] are subjected to attenuation of equal strength, but itmay also be used in those cases in which the two signals s₀ [t] and s₁[t] are attenuated to different degrees by the transmission channel, forexample with respective attenuation factors a₀ and a₁. In that case theautomatic gain control amplifier 1 is then to be used. The latterautomatically amplifies or attenuates the two received signals a₀ ·s₀[t]+n₀ [t] and a₁ ·s₁ [t]+n₁ [t] in such a way that the useful signalcomponents A.s₀ [t] and A.s₁ [t] in the output signal s₀ '[t]=A.s₀[t]+(A/a₀).n₀ [t] and s₁ '[t]=A.s₁ [t]+(A/a₁).n₁ [t] of the automaticgain control amplifier 1 become of equal magnitude. Therein n₀ [t] andn₁ [t] represent the interference signals which are present in differentstrengths in the receiver prior to the fading compensation or gaincontrol action at the frequencies f₀ and f₁ and A represents aproportionally constant.

FIGS. 3 and 4 each show a diagram of the frequency spectra which arepresent in a receiver prior to and after the gain control or fadingcompensation action, in respect of interference signals and usefulsignals which are attenuated to different degrees. Prior to the gaincontrol or fading components effect for example the received firstsignal s₀ [t] which is heavily attenuated in the transmission channeland thus also its frequency spectrum S₀ [f] are significantly weakerthan the received second signal s₁ [t] or the frequency spectrum S₁ [f]thereof. In addition n₀ <n₁. Otherwise FIG. 3 corresponds to FIG. 1.Thus, upon reception of the signals s₀ [t] and s₁ [t] which areattenuated to different degrees, prior to the separation in respect offrequency thereof at the input of the receiver, the signal s₀ [t] whichis most greatly attenuated is so amplified by the automatic gain controlamplifier 1, and the signal s₁ [t] which is most weakly attenuated is soattenuated, that both signals s₀ [t] and s₁ [t] become approximatelyequal before they are separated from each other in terms of frequency bymeans of the bond pass filters 2 and 5. In that respect the first signals₀ [t] and the associated interference signal n₀ [t] is amplified and atthe same time the second signal s₁ [t] and the associated interferencesignal n₁ [t] is attenuated, more specifically in such a way thatfinally the useful signal components A.s₀ [t] and A.s₁ [t] in the outputsignal of the automatic gain control amplifier 1 and therewith also theamplitudes of their frequency spectra S'₀ [f] and S'₁ [f] again becomeapproximately equal. The noise power density spectra n₀ and n₁ of theinterference signals n₀ [t] and n₁ [t] are in that case simultaneouslyamplified to n'₀ and attenuated to n'₁ respectively. Then, in terms ofvalue, the amplitudes of S'₀ [f]=S'₁ [f] lie between the amplitudes ofS₀ [f] and S₁ [f]. As can be seen from FIG. 4, that then again gives astarting position which is the same as the position shown in FIG. 1 inwhich there are identical useful signal strengths and differentinterference power densities, with this time n'₀ >n'₁.

I claim:
 1. A demodulation process for binary data which are transmittedby means of a frequency shift keying process by way of a transmissionchannel, wherein two shifted transmitted sinusoidal signals (s₀ (t), s₁(t) of different frequencies (f₀, f₁), after reception, are firstseparated from each other in terms of frequency using bandpass filtermeans (2, 5) and then separately amplitude-modulated using envelopecurve detection means (3, 6) for the purposes of producing two envelopecurve signals (z₀ (t), z₁ (t)), characterized in that the values of thefrequencies (f₀, f₁) of the two signals (s₀ (t), s₁ (t)) are selected tobe so far apart that the latter are disturbed independently of eachother and that at least one of the two frequencies (f₀, f₁) lies in aweakly disturbed frequency range of the transmission channel, that thetwo envelope curve signals (z₀ (t), z₁ (t)) are sampled once per bitusing a sampling circuit means (4, 7) for the purpose of producing theirsample values (z₀ (kT_(b)), z₁ (kT_(b))), that the sample values (z₀(kT_(b)), z₁ (kT_(b))), are passed to a calculator unit (8) in whosememory values of a decision table are stored, which values are derivedfrom the values of a probability table, that for the purposes of drawingup the probability table the value range of the sample values (z₀(kT_(b)) and z₁ (kT_(b))) of each respective envelope curve signal (z₀(t) and z₁ (t)) is each in itself divided by means of threshold values(w₀,i with i=0,1,2, . . . , N₀ and w_(ij) with j=0,1,2, . . . , N₁) intoa plurality (N₀ and N₁ respectively) of quantisation intervals which areplotted along respective ones of two coordinate axes of the probabilitytable for the purposes of forming the table areas (i;j) thereof, thatfor each table area (i;j) of the probability table a first probabilityvalue (P₀ (i,j)) and a second probability value (P₁ (i,j)) is calculatedand specified in the respective table area (i;j), wherein the firstprobability value (P₀ (i,j)) is the probability that the sample values(z₀ (kT_(b)), z₁ (kT_(b))) lie in the respective table (i;j) if thefirst signal (s₀ [t]) were sent and the second probability value (P₁(i,j)) is the probability that the sample values (z₀ (kT_(b)), z₁(kT_(b)) lie in the respective table area (i;j) if the second signal (s₁(t)) were sent, that a first logic value ("0") representing the firstsignal (s_(o) (t)) is set down in a table area (i;j) of the decisiontable which has the same threshold values (w₀,i, w₁,j) and as many(N₀.N₁) table areas (i;j) as the probability table if the firstprobability value (P₀ (i,j)) is greater than the second probabilityvalue (P₁ [i,j]), and a second logic value ("1") representing the secondsignal (s₁ (t)) is set down if the first probability value (P₀ (i,j)) isless than or equal to the second probability value (P₁ (i,j)), and thatthe calculator unit (8) ascertains in which table area (i;j) of thedecision table the supplied sample value (z₀ (kT_(b))), z₁ (kT_(b)))lie, whereupon it is then deduced from the logic value ("0" or "1")contained in the respective table area (i;j) of the decision tablewhether the first or the second signal (s₀ (t) or s₁ (t)) was mostprobably sent and is therefore to be considered as the received signal.2. A demodulation process according to claim 1 characterized in that forthe reception of signals (s₀ (t),s₁ (t) which are attenuated todifferent degrees, prior to the separation thereof in terms of frequencyat the input of a receiver the most heavily attenuated signal (s₀ (t))is so amplified using amplification means (1) and the most weaklyattenuated signal (s₁ (t)) is so attenuated that both signals (s₀ (t),s₁ (t)) become at least approximately equal before they are separatefrom each other in respect of frequency.
 3. A demodulation processaccording to claim 1 or claim 2 whereby the probability values (P₀(i,j), P₁ (i,j)) contained in the probability table are stored in thememory of the calculator unit (8) in order for them to be taken intoaccount in ascertaining the signal (s₀ (t) or s₁ (t)) which was mostprobably sent.
 4. A demodulation process according to claim 1 or claim 2whereby the logarithms of the probability values (P₀ (i,j), P₁ (i,j)contained in the probability table are stored in the memory of thecalculator unit (8) in order for them to be taken into account inascertaining the signal (s₀ (t) or s₁ (t)) which was most probably sent.